Re: battery voltage
The value at the volt meter is subject to all sorts of parallel parasitic draw off of the other things that run on that battery - ignition for sure, probably lights - basically *anything* that's ON when the key is ON.
You'll have to learn the OK voltage for your electrical setup and gauge.
If you measure AT the battery, you'll get a much better reading. See how that compares to the gauge.
On my boat, running/charging, I see ~13V at the meter. Turn on the lights, which don't draw that much - but parallel off the same circuit, and I'll drop to 12.7 or so...
Measured at the battery, I see 12.2-12.7 (not charging)
12.9-13.7 charging/running.